# IGCSE Maths Geometry Transformation

Printable View

• Apr 30th 2010, 01:14 AM
josemalawi
IGCSE Maths Geometry Transformation
Triangle ABC, A(2,1) B(7,1) C(2,4); transform the triangle by the matrix(1 -1 next row 1 1) and the transformation is a rotation followed by an enlargement. How to calculate the angle of the rotation and the scale factor of the enlargement. Thank You..
• Apr 30th 2010, 09:57 AM
wilbursmith
I think this post belongs to university math, linear and advanced algebra.
• May 1st 2010, 07:20 AM
josemalawi
I saw this in one of the IGCSE text...(Happy)
• May 1st 2010, 11:02 PM
wilbursmith
Okay, I just thought you might get some answers easier there. Actually, I should know the answer but I guess IŽll have to admit, I forgot ho to do it :(

Good luck!
• May 1st 2010, 11:35 PM
Debsta
Quote:

Originally Posted by wilbursmith
Okay, I just thought you might get some answers easier there. Actually, I should know the answer but I guess IŽll have to admit, I forgot ho to do it :(

Good luck!

A rotation matrix has the form
[cos x -sin x
sin x cos x ]
You can write your matrix as
sqrt(2) [ 1/sqrt(2) -1/sqrt(2)
............ 1/sqrt(2) 1/sqrt(2)]

Hence the angle of rotation is pi/4 radians, and the dilation factor is sqrt(2)
• May 2nd 2010, 07:00 AM
josemalawi
thank you sir;
• May 5th 2010, 04:03 PM
Gusbob
Quote:

Originally Posted by josemalawi
I saw this in one of the IGCSE text...(Happy)

There is a way to derive the rotation geometrically without the use of linear algebra.

I did this some time ago for fun (sorry about the ironically wrong orientation of the attachment :( )